consider a cart being pulled up an inclined plane by a student during a Physics lab. The applied force on the cart is 18 N is directed parallel to the incline to cause the cart to be displaced parallel to the incline for a given displacement of 0.7 m. The initial energy plus the work done by the external force equals the final energy. If the cart begins with 0 Joules of energy, and the student does 12.6 Joules of work (F•d•cosine of angle = 18 N•0.7 m•cosine 0 degrees = 12.6 J), then the cart will finish with 12.6 Joules of mechanical energy. The final energy (12.6 J) is equal to the initial energy (0 J) plus the work done by external forces (12.6 J).

Question

consider a cart being pulled up an inclined plane by a student during a Physics lab. The applied force on the cart is 18 N is directed parallel to the incline to cause the cart to be displaced parallel to the incline for a given displacement of 0.7 m. The initial energy plus the work done by the external force equals the final energy. If the cart begins with 0 Joules of energy, and the student does 12.6 Joules of work (F•d•cosine of angle = 18 N•0.7 m•cosine 0 degrees = 12.6 J), then the cart will finish with 12.6 Joules of mechanical energy. The final energy (12.6 J) is equal to the initial energy (0 J) plus the work done by external forces (12.6 J).

I am just wondering, how would the situation differ if there had been friction acting in the opposite direction on the cart?
would the mechanical energy possessed by the cart be less?

Answer 1

If there was friction acting in the opposite direction on the cart, the situation would indeed differ. Friction is a force that opposes motion, and in this case, it would act opposite to the direction of displacement. Therefore, it would do work against the applied force, reducing the amount of work done by the external force and subsequently the mechanical energy possessed by the cart.

To calculate the effect of friction on the mechanical energy of the cart, you would need to know the magnitude of the frictional force acting on the cart and the distance over which it acts. The work done by friction can be calculated using the equation W = F * d, where W is the work done, F is the magnitude of the force, and d is the distance over which the force acts.

Assuming the frictional force is constant throughout the displacement, the work done by friction would be the frictional force multiplied by the distance. This work done by friction would subtract from the work done by the external force, causing a decrease in the mechanical energy possessed by the cart.

So, if there was friction acting in the opposite direction on the cart, the mechanical energy possessed by the cart would be less than 12.6 Joules. The exact value would depend on the magnitude of the frictional force and the distance over which it acts.