You push a heavy luggage trolley of mass 80 kg with a force of 100 N. The trolley was initially at rest and after 4 seconds,it has a speed of 3 m/s. If friction is the only other horizontal force on the trolley apart from the force you exert, find the friction force in the direction of motion of the trolley.
Question
You push a heavy luggage trolley of mass 80 kg with a force of 100 N. The trolley was initially at rest and after 4 seconds,it has a speed of 3 m/s. If friction is the only other horizontal force on the trolley apart from the force you exert, find the friction force in the direction of motion of the trolley.
Solution
To solve this problem, we need to use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
Step 1: Calculate the acceleration of the trolley.
Acceleration is the change in velocity over time. The trolley starts from rest and reaches a speed of 3 m/s in 4 seconds. So, its acceleration (a) is:
a = (final velocity - initial velocity) / time a = (3 m/s - 0 m/s) / 4 s = 0.75 m/s²
Step 2: Calculate the net force acting on the trolley.
According to Newton's second law, the net force (F_net) is:
F_net = mass * acceleration F_net = 80 kg * 0.75 m/s² = 60 N
Step 3: Calculate the friction force.
The net force is the vector sum of all the forces acting on the trolley. In this case, the forces are the force you exert (F_you) and the friction force (F_friction). They act in opposite directions, so we can write:
F_net = F_you - F_friction
We can rearrange this equation to solve for the friction force:
F_friction = F_you - F_net F_friction = 100 N - 60 N = 40 N
So, the friction force acting on the trolley in the direction of its motion is 40 N.
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