A steel block weighing 12N is pulled up an incline plane 20° above the horizontal by a constant force of 7.35 N which makes an angle of 10° above the inclined plane. The block stars from rest and is pulled 2.0m along the inclined plane. the coefficient of friction between the block and inclined plane is 0.20.find the increase in kinetic energy of the block?
Fp = 12*sin20 = 4.1 N. = Force parallel with incline,
Fn = 12*Cos20 - 7.35*sin10 = 10 N. = Normal force,
Fk = u * Fn = 0.2 * 10 = 2 N.,
F = 7.35*Cos10 - Fp - Fk = 7.24 - 4.1 - 2 = 1.14 N. = Net force,
Work = F * d = 1.14 * 2 = 2.28 J. = Increase in KE.
damon is correct. change this to read...
finding pulling force: 7.35cos10 up the plane
finding pulling normal force: 7.35sin10 upwards
finding total normal force; 12sin20-7.35sin10
finding friction= mu*(above normal force)
work done by pulling: 7.35cos10*2
work absorbed by friction: mu(above normal force)*2
gain in PE: 12*2*sin20
KE= workdonebypulling-workabsorbedby friction-gain in PE
finding pulling force: 7.35cos10 up the plane
finding pulling normal force: 7.35sin10 upwards
finding total normal force; 12sin20-7.35sin10
finding friction= mu*(above normal force)
work done by pulling: 7.35cos10*2
work absorbed by friction: mu(above normal force)*2
KE= workdonebypulling-workabsorbedby friction.
- gain in potential energy due to going up
Yes
2.27j
To find the increase in kinetic energy of the block, we first need to find the work done on the block. Work is calculated by the formula:
Work = Force × distance × cos(θ)
Where:
Force = component of the force parallel to the displacement
distance = displacement along the inclined plane
θ = angle between force and displacement
First, let's find the component of the force parallel to the displacement. We can find this by using trigonometry. The force parallel to the displacement is given by:
Force parallel = Force × sin(θ force)
Where:
Force = 7.35 N (given)
θ force = angle of the force above the inclined plane = 10°
Substituting the values, we get:
Force parallel = 7.35 N × sin(10°)
= 1.28 N (approximately)
Next, let's calculate the distance along the inclined plane, which is given as 2.0m.
Now, let's find the angle between the force and displacement, θ. It is the angle between the force and the inclined plane, which is given as 20°.
Finally, we can calculate the work done on the block using the formula mentioned earlier:
Work = Force parallel × distance × cos(θ)
= 1.28 N × 2.0 m × cos(20°)
Now, let's calculate the coefficient of friction force. The friction force is given by:
Friction force = coefficient of friction × normal force
The normal force can be calculated by:
Normal force = Weight × cos(θ)
Where:
Weight = 12 N (given)
θ = angle of the inclined plane = 20°
Substituting the values, we get:
Normal force = 12 N × cos(20°)
Now, substituting the value of the normal force and coefficient of friction, we can find the friction force:
Friction force = 0.20 × Normal force
Finally, to find the increase in kinetic energy, we need to subtract the work done against friction (negative work) from the total work done:
Increase in kinetic energy = Work - Friction force × distance
Substituting the values, we can now calculate the increase in kinetic energy.