more problems?

Question

problem 1:
A ball on the end of a string is cleverly revolved at a uniform rate in a vertical circle of radius 75.0 cm. Its speed is 4.00 m/s and its mass is 0.300 kg.

(a) Calculate the tension in the string when the ball is at the top of its path.
________ N
(b) Calculate the tension in the string when the ball is at the bottom of its path.
_______N



problem 2:
A 970 N crate rests on the floor.
(a) How much work is required to move it at constant speed 6.7 m along the floor against a friction force of 180 N?
________ J
(b) How much work is required to move it at constant speed 6.7 m vertically?
________J

Answer 1

Maybe not quite so many pictures, but a good calculator would still help.

Answer 2

problem 1 : at the top of the path the ball experts three forces : P , T
P + T = m*a (all are vectors, a is accelerator)
on the direction of radius we have : P+T = m* v^2 / r
=> T = m*v^2/r - P = m*(v^2 / r - g) = 0.3 * (4^2 / 0.75 - 10 )= 3.4N
at the bottom , we also have this P + T = m*a (all are vectors)
on the direction of radius we have : T - P= m * v^2 / r
=> T = P + m*v^2/r = m(g+v^2/r) = 9.4N
problem 2 :
(a) we have this F(pull) + F1(friction) = 0 (all are vectors)
on the vertical direction : F - F1 = 0 => F = F1 = 180N
(b) we have this F + P = 0 (all are vectors)
on the horizontal direction : F - P = 0 => F = P = 970N

with the problem 2 : I need t ( time ) to calculate work A = F*s

Answer 3

Problem 1:

Given: r=75cm=0.75m
m=0.300kg
v=4.00m/s

Given mass,m=0.300kg,
weight =mg=0.300*9.8
=2.94N

Use the formula F=mv^2/r to get the centripetal force:

F=0.300*4^2/.75
=6.4N

a) At the top of its path the weight is opposite F.
Tension =F-weight
=6.4-2.94
=3.46N
b)At the bottom of its path the weight is in same direction as F. Tension=F+weight
=6.4+2.94
=9.34N

Problem 2:

a.) Work =f*s, where f is the friction force and s is the displacement of 6.7m. substitute:

Work=180*6.7
=1206 Joules

b)Same formula, but now the force is equal to the weight which is in the vertical direction:

Work=970*6.7
=6499 Joules

Answer 4

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