The problem goes like this...
You are pushing a shopping cart at a constant speed. The handle makes an angle of 30.0 degrees with the horizontal and the friction in the cart has a coefficient of 0.400 to account for all the axles, etc. The mass of the cart is 45.0-kg and we are pushing it a distance of 35.0 meters along a level floor. Find the "normal" force and the work due to that force.
I know that the answers are 573 N and 0 J respectively but I don't know how to get these answers. Please help!
normal force: weight of the cart+downward component of pushing.
fn=mg+F*sin30
friction= mu*fn
you did not state the pushing force value.
No work is done by the normal force, because the cart does not go in that direction.
Thanks, I got that far but the question was asked exactly as I wrote it. My teacher did not include a pushing force value. Can you think of any way to find the normal force without it?
Sure: Go to the market and get a crystal ball that can see inside your teacher's mind. The question is flawed.
Alright, but thanks anyway!
To solve for the normal force and the work due to that force, we need to break down the problem into several steps.
Step 1: Analyze the forces acting on the cart.
Since the cart is on a level floor and moving at a constant speed, there are two forces to consider: the force of gravity and the force of friction.
- The force of gravity: This force acts vertically downward and is equal to the weight of the cart, given by the formula F_gravity = m * g, where m is the mass of the cart (45.0 kg) and g is the acceleration due to gravity (9.8 m/s²).
- The force of friction: This force opposes the motion of the cart and acts parallel to the surface. The formula for the force of friction is F_friction = µ * N, where µ is the coefficient of friction (0.400) and N is the normal force.
Step 2: Find the normal force.
The normal force, denoted by N, is the force exerted by a surface perpendicular to the object in contact with it. In this case, the horizontal floor exerts an equal and opposite normal force to counteract the force of gravity.
Since the cart is on a level floor and there is no vertical acceleration, the normal force must balance out the force of gravity. Therefore, N = F_gravity = m * g.
Plugging in the given values, we get N = (45.0 kg) * (9.8 m/s²) = 441 N.
Step 3: Calculate the work due to the normal force.
The work done by a force is given by the formula W = F * d * cosθ, where F is the force applied, d is the displacement, and θ is the angle between the force and the direction of motion.
In this case, the normal force is perpendicular to the displacement, so the angle θ is 90 degrees. Since cos(90°) = 0, the work done by the normal force is zero (0 J).
Therefore, the answers are:
Normal force (N) = 441 N
Work due to the normal force (W) = 0 J