Question

The loaded 150-kg skip is rolling down the incline at 4 m/s when a force P is applied to the cable as shown at time t=0. The force P is increased uniformly with the time until it reaches 600 N at t=4 s, after which time it remains constant at this value. Calculate (a) the time t ′

at which the skip reverses its direction and (b) the velocity v of the skip at t=8 s. Treat the skip as a particle.

Answer 1

To find the time at which the skip reverses its direction, calculate the acceleration using the applied force. The velocity of the skip at t = 8s can be found using the initial velocity and the acceleration.

Step-by-step explanation:

To find the time at which the skip reverses its direction, we need to calculate the acceleration of the skip. The force P applied to the cable can be divided into two parts: one due to gravity and the other due to the applied force. The force P due to gravity can be calculated using the equation F = mg, where m is the mass of the skip and g is the acceleration due to gravity. The force P due to the applied force can be found using P = ma, where a is the acceleration of the skip. Since the force P increases uniformly with time, we can find the acceleration using the equation a = (deltaP)/delta(t), where deltaP is the change in force and delta(t) is the change in time.

Once we have the acceleration, we can find the time t' at which the skip reverses its direction by setting the acceleration equal to zero. At this point, the net force on the skip is zero, causing it to change direction. To find the velocity of the skip at t = 8s, we can use the equation v = u + at, where u is the initial velocity of the skip and a is the acceleration of the skip.