4. What force is needed to push a 15 N object up a 20° incline at constant speed when the coefficient of friction is 0.30?
Compute the friction force,
Ff = W*cos20*Uk
Add it to the component of the weight in the direction down the incline:
W sin20.
The applied force must equal the sum of those two forces if the object is yo move at constant speed up the incline.
Uk = 0.30
W = 15 N
To calculate the force needed to push an object up an incline at constant speed, we need to consider the gravitational force acting downwards, the frictional force acting against the motion, and the force component required to counteract the gravitational force along the incline.
1. First, we calculate the force component needed to counteract the gravitational force along the incline. This force is given by the formula:
Force along incline = Weight of the object * sin(θ)
Where:
Weight of the object = mass * acceleration due to gravity = 15N (given)
θ = angle of the incline = 20° (given)
Plugging in the values, we have:
Force along incline = 15N * sin(20°)
2. Next, we calculate the frictional force opposing the motion. This force is given by the formula:
Frictional force = coefficient of friction * Normal force
The Normal force is the perpendicular force exerted by the surface on the object, which is equal to the weight of the object. So:
Normal force = weight of the object = 15N
Plugging in the value of the coefficient of friction (0.30), we have:
Frictional force = 0.30 * 15N
3. Finally, the force needed to push the object up the incline at constant speed is the sum of the force along the incline and the frictional force:
Total force needed = Force along incline + Frictional force
Plugging in the calculated values, we have:
Total force needed = 15N * sin(20°) + (0.30 * 15N)
Calculating this expression will give us the force needed to push the 15 N object up the 20° incline at constant speed when the coefficient of friction is 0.30.