Most Important Force And Motion Quiz Test Online | Physics

Using KE = p²/(2m), for a constant momentum 'p', kinetic energy is inversely proportional to mass. Thus, the lighter body (smaller m) has more kinetic energy.

Newton's second law can be stated as F = Δp/Δt, meaning the net force is equal to the rate of change of momentum.

Using the relationship KE = p²/(2m), if momentum 'p' is doubled to '2p', the new kinetic energy becomes (2p)²/(2m) = 4p²/(2m), which is four times the original.

In any collision within an isolated system, momentum is conserved. In an inelastic collision, some kinetic energy is converted to other forms (heat, sound).

The centripetal force is always perpendicular to the direction of motion (the velocity vector). Since W = Fd cos(90°), the work done is zero.

The change in momentum is equal to the impulse, which is Force × time. Δp = 5 N * 0.1 s = 0.5 Ns or 0.5 kg m/s.

From PE = mgh, we get h = PE / (mg) = 1 J / (1 kg * 9.8 m/s²) ≈ 0.102 m.

Newton's second law (F=ma) provides a quantitative relationship to measure force based on the mass and acceleration of an object.

Instantaneous velocity is the derivative of displacement with respect to time, which is defined as the limit of the average velocity as Δt → 0.

Kinetic energy (KE = ½mv²) is proportional to the square of the velocity. If v becomes 2v, KE becomes ½m(2v)² = 4(½mv²).

Horsepower is a non-SI unit of power, where 1 hp is approximately equal to 746 watts.

Constant velocity means acceleration is zero. According to F=ma, if acceleration is zero, the net force must also be zero.

The conservation of linear momentum is a fundamental principle that holds for any isolated system, meaning a system with no net external force acting on it.

The work-energy theorem provides a direct link between the net work done on an object and the change in its kinetic energy (W_net = ΔKE).

Using the equation of motion s = v_i*t + ½at², with v_i = 0, s = ½(9.8)(4)² = 0.5 * 9.8 * 16 = 78.4 m.

In classical mechanics, mass is an intrinsic, constant property of an object. A force can change its motion or shape, but not its mass.

The combination of constant horizontal velocity and constant vertical acceleration due to gravity results in a parabolic path.

At the highest point of its trajectory, the instantaneous vertical velocity is zero, but the acceleration due to gravity (g ≈ 9.8 m/s²) is still acting on it, pointing downwards.

The horizontal range of a projectile is the same for complementary angles of projection (angles that add up to 90°), such as 30° and 60°.

The distance covered in the nth second is proportional to (2n-1). For n=1, it's 1. For n=2, it's 3. Thus, the ratio is 1:3.

In a perfectly inelastic collision, the objects stick together after impact, meaning their relative velocity of separation is zero. The coefficient of restitution e is the ratio of relative separation velocity to relative approach velocity, so e=0.

Newton's First Law describes an object's tendency to resist changes in its state of motion, which is the definition of inertia.

Using the law of cosines for vector addition, R² = A² + B² + 2ABcosθ. If R=A=B, then A² = A² + A² + 2A²cosθ, which simplifies to cosθ = -1/2. Thus, θ = 120°.

Force is a vector quantity, and as such, it requires both a magnitude (how strong it is) and a direction to be fully described.

The time of flight is the total time the projectile is in the air. It is twice the time taken to reach the maximum height, which is (v_i sinθ)/g.

The force exerted by the person is vertically upwards to counteract gravity, while the displacement is horizontal. The angle between them is 90°, and since W = Fd cos(90°), the work done is zero.

Retardation (deceleration) means the velocity is decreasing. A decreasing velocity is represented by a negative slope on a velocity-time graph.

For a variable force, the work done is the integral of F with respect to displacement, which is geometrically represented by the area under the Force-Displacement graph.

The normal force (apparent weight) must support the true weight (mg) and also provide the upward acceleration (ma). Thus, N = mg + ma = m(g+a).

Uniform motion implies constant velocity. Therefore, the velocity does not change over time.

Escape velocity is the minimum speed an object needs to break free from a planet's gravitational pull without further propulsion. For Earth, this is about 11.2 km/s.

This formula relates the initial vertical velocity component to the maximum height reached against gravity, derived from v_f² = v_i² + 2as.

The value of 'g' is slightly greater at the poles than at the equator due to the Earth's shape and rotation. Since Weight = mg, the weight increases.

Relative to the car's frame of reference, the man is not changing his position. Therefore, his speed with respect to the car is zero.

An explosion is caused by internal forces. In the absence of external forces, the total momentum of the system (the rock pieces) is conserved.

The work done by a conservative force (like gravity) between two points depends only on the initial and final positions, not on the path followed between them.

Using s = v_i*t + ½gt², with v_i = 0, the distance is s = ½(9.8)(2)² = 19.6 m.

Displacement is a vector (start to end point), while distance is a scalar (total path). An object can travel a non-zero distance and return to its starting point, making its displacement zero while distance non zero.

The change in momentum (impulse) is calculated as Force × time. Δp = 100 N × 10 s = 1000 Ns or 1000 kg m/s.

Action-reaction pairs act on the two different interacting bodies. Forces can only cancel out if they act on the same body.

Since p = √(2m(KE)), if KE is constant, then momentum 'p' is directly proportional to the square root of mass, √m.

The net downward force (mg - N) provides the downward acceleration (ma). The apparent weight (Normal force N) is N = mg - ma = m(g-a).

According to Newton's Second Law (F_net = ma), if the net force (the vector sum of all forces) is zero, the acceleration must be zero. This is the condition for equilibrium.

This is a direct application of Newton's second law, F=ma. So, a = F/m = 1 N / 1 kg = 1 m/s².

When KE is halved, the other half (490/2 = 245 J) is converted to potential energy. Using PE = mgh, h = PE/mg = 245 / (2 * 9.8) = 12.5 m.

Since Power = Work/time = (Force ⋅ displacement)/time, and velocity = displacement/time, Power = Force ⋅ velocity.

This phenomenon is due to inertia. The passenger's body continues to move forward with the bus's initial velocity while the bus itself stops.

Constant velocity means zero acceleration. From F=ma, if acceleration is zero, the net force on the object must also be zero.

The horizontal range is the same for complementary angles of projection (angles that sum to 90°), such as 30° and 60°.

Average speed for equal distances is the harmonic mean: V_avg = 2v1v2 / (v1 + v2) = 2(30)(50) / (30 + 50) = 3000 / 80 = 37.5 km/hr.

Force is the rate of change of momentum. F = Δp/Δt = (mΔv)/Δt = (0.15 kg * 20 m/s) / 0.1 s = 30 N.

Momentum (p = mv) and Impulse (I = FΔt) both have the dimensions [MLT⁻¹]. The impulse-momentum theorem states that they are equivalent.

Weight is the force of gravity acting on a mass (Weight = mg). The S.I. unit for force is the Newton (N).

For θ = 45°, R_max = v_i²/g and H = v_i²(sin²45)/(2g) = v_i²/(4g). Therefore, H = R_max / 4.

First, find the distance: d = v × t = 2 m/s × 5 s = 10 m. Then, work done W = F × d = 10 N × 10 m = 100 J.

When released, the ball has the same orbital velocity as the satellite. It effectively becomes a new, independent satellite in the same orbit, moving alongside the original one.

In uniform circular motion, the velocity vector is always tangent to the circle, while the centripetal acceleration vector is always directed towards the center. Thus, they are always perpendicular.

A non-conservative force is one where the work done depends on the path taken. Friction is a classic example as it dissipates mechanical energy as heat.

The resultant force must be between the minimum possible value (4N - 3N = 1N) and the maximum possible value (4N + 3N = 7N). 8N is outside this range.

By momentum conservation, 3*16 + 6*v = 0, so v = -8 m/s. The kinetic energy of the 6 kg mass is KE = ½mv² = ½(6)(-8)² = 192 J.

A 300% increase means the new KE is 4 times the original. Since p = √(2m(KE)), the new momentum will be √4 = 2 times the original, which is a 100% increase.

The centripetal force is always perpendicular to the displacement, so the work done by this force is zero. Also, since speed is constant, the kinetic energy does not change, meaning no net work is done.

Since momentum is proportional to the square root of kinetic energy (p = √2m(KE)), doubling the KE means the new momentum will be √2 times the original momentum.

The second equation of motion relates displacement (s), initial velocity (v_i), time (t), and uniform acceleration (a).

The force is the rate of change of momentum. The total momentum imparted to the bullets per second is (n * m * v). This is the magnitude of the reaction force on the gun.

This is a form of projectile motion. The constant horizontal velocity and constant vertical acceleration due to gravity combine to form a parabolic trajectory.

An isolated system is defined as a system with no net external force. In such a system, the total linear momentum is always conserved.

By conservation of momentum, m_gun * v_gun = m_bullet * v_bullet. So, m_gun = (0.05 kg * 30 m/s) / 1 m/s = 1.5 kg.

The change in momentum is Δp = m(v_f - v_i) = 0.5(10 - (-10)) = 10 kg m/s. The force is F = Δp / Δt = 10 / 0.01 = 1000 N.

Work is the dot product of the force and displacement vectors: W = F ⋅ d = (2)(4) + (3)(-2) = 8 - 6 = 2 J.

Due to inertia (Newton's First Law), the stone will continue to move in the direction of its instantaneous velocity at the moment the centripetal force from the string disappears. This direction is tangent to the circle.

Ignoring air resistance, the ball retains the car's constant horizontal velocity. It travels horizontally along with the car while moving vertically, landing back in the person's hand.

A rocket expels mass (exhaust gas) at high velocity in one direction. By the conservation of momentum (and Newton's Third Law), the rocket gains an equal amount of momentum in the opposite direction.