An object is pulled up an incline plane at a constant velocity as the picture above shows. Calculate the tension on the rope.
1 answer:
Hi there!
Since the object is being pulled at a constant velocity, the forces must be balanced.
Since there is no movement vertically, we must take into account the horizontal forces. We can also assume a positive acceleration to be in the direction of motion.
The acceleration and force due to gravity on an incline is:
a = gsinФ
F = MgsinФ
∑F = -MgsinФ + T
Since it is getting pulled at a constant velocity, ∑F = 0. So:
0 = -MgsinФ + T
MgsinФ = T
Solve for T by plugging in values. Let g = 10 m/s²
T = (120)(10)sin(27) ≈ 545 N
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The force applied by the man is 60 N
Explanation:
We can solve this problem by applying Newton's second law, which states that:
(1)
where
is the net force acting on the child+cart
m is the mass of the child+cart system
a is their acceleration
In this problem, we have:
m = 30.0 kg is the mass
And there are two forces acting on the child+cart system:
- The forward force of pushing, F
- The force resisting the cart motion, R = 15.0 N
Therefore we can write the net force as
where R is negative since its direction is opposite to the motion
So eq.(1) can be rewritten as
And solving for F,
Learn more about Newton's second law:
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