A shopper pushes a grocery cart 20m at constant speed on level ground against a 35N frictional force. He pushes in a direction 25 degrees below the horizontal. What is the work done on the cart by gravity?

I know you can use W=Fdcos(theta) where F=mass*gravity. BUT, no mass is given so there must be some other way.

Help!

mass is not required. Constant speed means zero acceleration.

Fcos(theta) - Ff=m*a
Fcos(theta) - Ff=0
F cos(25) =35
0.9063F=35
F=38.62N
W=Fcos(theta)*d
W= 38.62 cos(25)*20
W=700J

gravity is doing no work because its perpendicular to the motion

Yes, you are correct that you can use the formula W = F * d * cos(theta) to calculate the work done on the cart by gravity. However, since the mass of the cart is not given, we need to find an alternative approach.

In this case, we can calculate the work done on the cart by gravity using the concept of potential energy. The work done by gravity is equal to the change in gravitational potential energy.

The formula for gravitational potential energy is given by PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the vertical height.

Since the cart is on level ground, there is no change in vertical height, and therefore the change in gravitational potential energy is zero. As a result, the work done on the cart by gravity is also zero.

So, in this scenario, the work done on the cart by gravity is zero.

To find the work done on the cart by gravity, we can use the gravitational force formula instead of the mass.

The gravitational force is given by the formula F = m * g, where m represents the mass of the object and g represents the acceleration due to gravity. Since the mass is not given in this case, we can proceed without it.

The work done on the cart by gravity can be calculated using the following formula:

W = F * d * cos(theta)

Where:
- W is the work done on the cart by gravity
- F is the force of gravity acting on the cart
- d is the displacement of the cart
- theta is the angle between the force of gravity and the displacement vector

Since we are interested in finding the work done on the cart by gravity, we need to determine the force of gravity acting on the cart. In this case, the force of gravity is equal to the weight of the cart.

Now, we just need to find the angle between the force of gravity and the horizontal displacement. The given information states that the shopper pushes the cart 25 degrees below the horizontal. Since the force of gravity acts vertically downward, the angle between the force of gravity and the horizontal is 90 degrees (perpendicular to the horizontal).

Using this information, we can substitute the known values into the equation:

W = F * d * cos(theta)
W = (m * g) * d * cos(90°)

Since cos(90°) = 0, the equation simplifies to:

W = (m * g) * d * 0

This means that the work done on the cart by gravity is 0.