Force and Motion Test. 4

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.

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

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

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

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).

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.

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

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.

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

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.

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

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

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

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.

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.

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.

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.

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.

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.