A block of mass m1 = 2 kg rests on a table with which it has a coefficient of friction µ = 0.53. A string attached to the block passes over a pulley to a block of mass m3 = 4 kg. The pulley is a uniform disk of mass m2 = 0.4 kg and radius 15 cm. As the mass m3 falls, the...
A certain non-uniform but cylindrically symmetric cylinder has mass 9 kg, radius 1.2 m, and moment of inertia about the center of mass 7.6 kg m2. It rolls without slipping down a rough 20° incline.
What is the acceleration of the cylinder's center-of-mass...
A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around it, and a m = 5 kg weight is hanging on the string. The system of the weight and disk is released from rest.
a) When the 5 kg weight is moving with a speed of 1.7 m/s, what is the kinetic energy of the...
A circus cannon, which has a mass M = 5000 kg, is tilted at q = 40°. When it shoots a projectile at v0 = 80 m/s with respect to the cannon, the cannon recoils along a horizontal track at vcannon = 1 m/s with respect to the ground.
1. At what angle to the horizontal...
A bullet of mass 0.008 kg and initial speed 300 m/s penetrates an initially stationary pop can of mass 0.042 kg and emerges with a speed 210 m/s.
What is the initial momentum of the bullet and pop can system?
What is the final momentum of the bullet...
The two problems below are related to a cart of mass M = 500 kg going around a circular loop-the-loop of radius R = 15 m, as shown in the figures. All surfaces are frictionless. In order for the cart to negotiate the loop safely, the normal force exerted by the track on...
A block of mass m = 3.5 kg rests on a frictionless floor. It is attached to a spring with a relaxed length L = 5 m. The spring has spring constant k = 12 N/m and is relaxed when hanging in the vertical position. The...
A spring is stretched a distance of Dx = 40 cm beyond its relaxed length. Attached to the end of the spring is an block of mass m = 8 kg, which rests on a horizontal frictionless surface. A force of magnitude 20 N is required to hold the block at this position. The force...
A car of mas m = 1000kg is sliding down a hill. The coefficients of friction between the car's tires and the ground are us=0.89 and uk=0.61. For what inclination angle will the car slide down the hill with a constant velocity?
The Attempt at a...
A block of mass m1 = 2 kg and a block of mass m2 = 3 kg are tied together and are pulled from rest across the floor by a force of P = 25 N. The coefficient of friction of the blocks with the floor is µ = 0.14.
I found the acceleration to be 3.6266 m/s2.
On a level road with its brakes on, the shortest distance in which a car traveling with 80 km/hr can stop is 95 m. This shortest distance occurs when the driver uses anti-lock brakes which means that that the car brakes without skidding.
I found the deceleration to be...
A 2 kg mass and a 3 kg mass are on a horizontal frictionless surface, connected by a massless spring with spring constant k = 140 N/m. A 15 N force is applied to the larger mass. How much does the spring stretch from...
I have to prove the following claim.
Claim: For any positive integers m and n, m and n both greater than 1, if n|m and a≡b(mod m), then a≡b(mod n).
The Attempt at a Solution
so i first changed each equation (ex: a≡b(mod m)) to a=b+qm and a=b+qn...
Three blocks on a horizontal frictionless table are connected with strings as shown below. The three blocks are pulled to the right with a force T3 = 60N. If m1 = 10kg, m2 = 20kg, and m3 = 30kg, find the tensions T1 and...
Three strings, in the horizontal plane, meet in a knot and are pulled with three forces such that the knot is held stationary. The tension in string 1 is T1 = 2.9 N. The angle between strings 1 and 2 is q12 = 130° and the angle between strings 1 and 3 is q13 = 120° with...
We say two ordered pairs p1=(x1,y1) and p2=(x2,y2) are perpendicular if and only if x1x2 +y1y2=0.
For any three ordered pairs p1, p2, and p3, if p1 is perpendicular to p2 and p2 is perpendicular to p3 then how would I show that p1 is parallel to p3?
I believe I need...
A car moving at a speed of 30 m/s enters a curve that describes a quarter turn of radius 114 m. The driver gently applies the brakes, giving a constant tangential deceleration of magnitude 1.2 m/s2.
a) Just before emerging from the turn, what is the magnitude of the...
A river 500 ft wide flows with a speed of 8 ft/s with respect to the earth. A woman swims with a speed of 4 ft/s with respect to the water.
1) If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?