You are trying to raise a bicycle wheel of mass m and radius R up over a curb of height h. To do this, you apply a horizontal force F S . What is the smallest magnitude of the force F S that will succeed in raising the wheel onto the curb when the force is applied (a) at the center of the wheel and (b) at the top of the wheel? (c) In which case is less force required?
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You are trying to raise a
bicycle wheel of mass m and radius
R
up over a curb of height h. To do
this, you apply a horizontal force F S
. What is the smallest
magnitude of the force F S that will
succeed in raising the wheel onto the
curb when the force is applied (a) at
the center of the wheel and (b) at the
top of the wheel? (c) In which case is less force required?
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- .) The figure shows a vertical force applied tangentially to a uniform cylinder of weight F. The coefficient of static friction between the cylinder P and all surfaces is 0.500. The force P is increased in magnitude until the cylinder begins to rotate. In terms of F, find the maximum force magnitude P that can be applied without causing the cylinder to rotate. Suggestion: show that both friction forces will be at their maximum values when the cylinder is on the verge of slipping.A bicycle wheel has a diameter of 64.9 cm and a mass of 1.86 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 9.04-cm-diameter sprocket in order to give the wheel an acceleration of 4.50 rad/s2? N(b) What force is required if you shift to a 5.67-cm-diameter sprocket? NFy Ex The plant in the picture has mass of 30 kg, and is hanging at a distance of 1.8 meters from the wall. The horizontal rod has mass of 7.8 kg. Assume that its weight is evenly distributed, therefore it can be treated as a single force at the center of mass. The rod is 2 meters long, and there is a cable at a 38° angle supporting it at the end. Using the wall as the axis of rotation, find the magnitude of the downward torque, from both the weight of the rod and the weight of the plant.
- A simple pendulum consists of a small object of mass 3.5 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point. (a) Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string makes a 7.0° angle with the vertical. (b) Does the torque increase or decrease as the angle increase?Force F = (-7.0 N)î + (5.0 N) ĵ acts on a particle with position vector7 = (4.0 m)î + (5.0 m) ĵ. (a) What is the torque on the particle about the origin, in unit-vector notation? = N: m (b) What is the angle between the directions of r and Torque is the cross product of a position vector (extending from a chosen point, here the origin, to the particle) and a force vector. Did you take the cross product in unit-vector notation? Do you remember how find the angle between two vectors by taking a dot product in both unit-vector notation and also in magnitude-angle notation? (You can similarly use a cross product to do this.) Do you remember how to find the magnitude of a vector from its components?Problem 8: A uniform ladder whose length is 5 meter and whose weight is 400 N leans against a frictionless vertical wall. The coefficient of static friction between the level ground and the foot of the ladder is 0.40. (a) The greatest distance (denoted x) the foot of the ladder can be placed from the base of the wall without the ladder immediately slipping is ________ (b) The torque of the weight relative to the foot of the ladder at such distance is _______
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- A man holds a 195-N ball in his hand, with the forearm horizontal (see the figure). He can support the ball in this position because of the flexor muscle force M , which is applied perpendicular to the forearm. The forearm weighs 20.7 N and has a center of gravity as indicated. Find (a) the magnitude of M and the (b) magnitude and (c) direction (as a positive angle counterclockwise from horizontal) of the force applied by the upper arm bone to the forearm at the elbow joint. Upper arm bone- Flexor muscle M Elbow cg joint 0.0510 m+ 0.0890 m -0.330 m- (a) Number i Units (b) Number i Units (c) Number i Units >A 75 kg man's arm, including the hand, can be modeled as a 79-cm-long uniform cylinder with a mass of 3.7 kg. In raising both his arms, from hanging down to straight up, by how much does he raise his center of gravity?