Another Question: Find the work done by the kinetic frictional force

[zizikaboo]

A 300N force is pulling an 90.0 kg refrigerator across a horizontal surface. The force acts at an angle of 22.0° above the surface. The coefficient of kinetic friction is 0.200, and the refrigerator moves a distance of 6.00 m.

i found out the work done by pulling force is 1669 J and its asking for the work done by the kinetic frictional force!
here's what i did but the answer is wrong though...i tried a million times and it's still wrong! i know something's wrong here and i know it's not the acceleration of gravity or m...hmm

i did
mg times mu=9.8*90*.2
then i times it by the distance to get work. 176.4N*6m=1058.4 J
which is WRONG! arghh...am i missing something here?

 

[ehild]

A 300N force is pulling an 90.0 kg refrigerator across a horizontal surface. The force acts at an angle of 22.0° above the surface. The coefficient of kinetic friction is 0.200, and the refrigerator moves a distance of 6.00 m.


i did
mg times mu=9.8*90*.2
then i times it by the distance to get work. 176.4N*6m=1058.4 J
which is WRONG!

The friction is equal the normal force multiplied by the coefficient of friction.

F_{fr} = \mu F_N

As the refrigerator slides on a horizontal plane the vertical component of the resultant force is zero. This vertical component is the normal force + vertical component of the pulling force - mg.

F_N+ F\sin (\alpha) - mg = 0.

ehild

 

[thepatientmental]

The correct way to calculate the work done by the kinetic frictional force is to use the formula W = Fd cosθ, where W is the work done, F is the force, d is the distance, and θ is the angle between the force and the displacement.

In this case, the force acting against the movement of the refrigerator is the kinetic frictional force, which is given by Ff = μN, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is equal to the weight of the refrigerator, so N = mg.

Plugging in the given values, we get Ff = (0.200)(90 kg)(9.8 m/s^2) = 176.4 N. Now, we can calculate the work done by the kinetic frictional force using the formula: W = Ff d cosθ = (176.4 N)(6.00 m)cos(180°) = -1058.4 J.

Note that the work done by the kinetic frictional force is negative because it is acting in the opposite direction of the displacement. This means that the kinetic frictional force is doing negative work, which is taking away energy from the system. Therefore, the total work done by all forces on the refrigerator is the sum of the work done by the pulling force (1669 J) and the work done by the kinetic frictional force (-1058.4 J), which is equal to 611.6 J.