Solve PCAT Physics Problem: Lawn Mower Force & Acceleration in 2.5s

[fishert16]

A person pushes a 14kg lawn mover at constant sped with a force of 88N directed along the handle, which is at an angle of 45 degress to the horizontal. (a) draw the Free-body diagram showing all forces acting on the mower. (b) Calculate the horizontal friction force on the mower, then (c) the normal force exerted vertically upward on the mower by the ground. (d) What force must the person exert on the lawn mower accelerate it from rest to 1.5m/s in 2.5 seconds, assuming the same friction force?

This is a problem on my practice PCAT test for Pharmacy school. And its been a while since I have had physics so any help would be appreciated.

Thanks

 

[denverdoc]

well here are some eqns to consider,

F=ma therefore if an object isn't accelerating the net forces are zero.
The "normal" force is the one from the Earth pushing upwards on the mower; from the above comment, if the mower isn't burrowing underground, the Normal force must then equal the weight of the mower plus whatever part of the push is directed vertically.

Vf=Vi+at (linear acceleration, relating time, initial and final velocities)

PS: I sympathize, I am myself brushing the rust off of 20 years of non-use since school. Sort of like riding a bike, but more like riding one with a blindfold, as I have had to reaquaint myself with all the tricks that were once second nature. Can be done, just in the future try to figure out what eqns might be relevant and some reasoning as to which ones might be most useful. You'll get a lot more help that way.

 

[m2003]

for reaching out for help with this physics problem. I am happy to assist you in solving it.

(a) The free-body diagram for this problem would show the forces acting on the lawn mower as follows: the force of 88N directed along the handle at a 45 degree angle, the weight of the lawn mower (mg) acting downwards, the normal force exerted by the ground upwards, and the frictional force acting in the opposite direction to the motion.

(b) To calculate the horizontal friction force, we can use the formula Ff = μN, where μ is the coefficient of friction and N is the normal force. Since the mower is moving at a constant speed, we can assume that the friction force is equal to the applied force of 88N. Therefore, Ff = 88N.

(c) To calculate the normal force, we can use the formula ΣFy = 0, where ΣFy is the sum of all the forces in the vertical direction. Since the mower is not accelerating in the vertical direction, the normal force must be equal to the weight of the mower, which is 14kg multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, N = 137.2N.

(d) To find the force needed to accelerate the mower, we can use the formula F = ma, where F is the force, m is the mass of the mower, and a is the acceleration. Since the mower is starting from rest and accelerating to a speed of 1.5 m/s in 2.5 seconds, the acceleration would be (1.5 m/s)/(2.5 s) = 0.6 m/s^2. Therefore, the force required to accelerate the mower would be F = (14 kg)(0.6 m/s^2) = 8.4N.

I hope this helps you solve the problem and refresh your understanding of physics concepts. Good luck on your PCAT test!