A trolley of mass of 20kg rolls down an incline from rest. The top of the incline is 10m above the ground. The trolley experiences a constant frictional force of 25N while it rolls down the incline. The velocity attained by the trolley at the bottom of the incline is 12m/s.
The question says calculate the displacement of the trolley along the incline. How do I calculate it?
10m
To calculate the displacement of the trolley along the incline, we can use the concept of work and energy. The work done on the trolley is equal to the change in its mechanical energy.
First, let's calculate the initial potential energy of the trolley at the top of the incline:
Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)
PE = 20 kg * 9.8 m/s^2 * 10 m
PE = 1960 J
Next, let's calculate the final kinetic energy of the trolley at the bottom of the incline:
Kinetic Energy (KE) = 0.5 * mass (m) * velocity^2
KE = 0.5 * 20 kg * (12 m/s)^2
KE = 1440 J
The work done on the trolley is equal to the change in its mechanical energy:
Work (W) = Change in Energy (ΔE) = KE - PE
W = 1440 J - 1960 J
W = -520 J
The negative sign indicates that work is being done against the trolley due to the frictional force. Now, let's calculate the work done by the frictional force:
Frictional Force (f) = force (F) * displacement (d)
25 N = F * displacement (d)
Since the frictional force is constant, we can use it to calculate the displacement:
displacement (d) = 25 N / F
displacement (d) = 25 N / 25 N
displacement (d) = 1 m
Therefore, the displacement of the trolley along the incline is 1 meter.