A block of weight 12 lbs is placed on a cart of weight 40 lbs that...

A block of weight 12 lbs is placed on a cart of weight 40 lbs that is attached to a spring with a constant of 500 lb/in. The coefficient of static friction between block A and cart B is 0.15, and the coefficient of friction between cart B and the ground is negligible.

a.) Find the maximum amplitude of oscillation of the system to prevent block A from sliding.

b.) Use conservation of energy to determine the maximum velocity and acceleration of the system.

c.) If the cart begins at the maximum amplitude to the right, determine the equation for x(t), v(t), and a(t). [Hint: The template for the equations are in your Physics I book/notes.

Expert Solution

Inorder to not slip between cart and block means that they will have common acceleration up to a point.

After that point they move with different accelerations and results in slipping.

Conservation of energy is used in finding max velocities.

Solution is uploaded below.

Ally Wells answered 11 months ago

A 12-lb weight is placed upon the lower end of a suspended spring. The weight comes...

A 12-lb weight is placed upon the lower end of a suspended spring. The weight comes to rest in its equilibrium position, stretching the spring by 1.5 inches. The weight is then pushed upward 2 inches above the equilibrium and released at t=0 with an initial velocity downward of 2ft/sec. Assume there is no damping caused by an external force a) Find the displacement of the weight function x(t) as a function of time, b) Determine the amplitude, period, and...

A 40-year-old woman, 5'4 "tall and 155 lbs. Wants to lose weight, for this reason she...

A 40-year-old woman, 5'4 "tall and 155 lbs. Wants to lose weight, for this reason she decided to consume no more than 1,600 calories daily. The first week she lost weight, however in the third week she noticed that she had gained more than the 5 lbs he had lost 1. Explain in physicochemical terms what happened in this situation.

In a weight loss programs, 40 adults used the Atkins weight loss program. After 12 months,...

In a weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8lb. Construct a 97% confidence interval of the mean weight loss.h

Differential Equations (FREE, UNDAMPED MOTION) A 12-lb weight is placed upon the lower end of a...

Differential Equations (FREE, UNDAMPED MOTION) A 12-lb weight is placed upon the lower end of a coil spring suspended from the ceiling. The weight comes to rest in its equilibrium position, thereby stretching the spring 1.5 in. The weight is then pulled down 2 in. Below its equilibrium position and released from rest at t = 0. Find the displacement of the weight as a function of time; determine the amplitude, period, and the frequency of the resulting motion. Assume...

a. Assume that the average weight of an NFL player is 245.7 lbs with a standard...

a. Assume that the average weight of an NFL player is 245.7 lbs with a standard deviation of 34.5 lbs. The distribution of NFL weights is not normal. Suppose you took a random sample of 32 players. What is the probability that the sample average will be greater than 250 lbs? Round your answer to three decimal places, eg 0.192. b. Assume that the average weight of an NFL player is 245.7 lbs with a standard deviation of 34.5 lbs....

A spring contains a weight of 32 lbs. It is stretched to a distance of 1.6...

A spring contains a weight of 32 lbs. It is stretched to a distance of 1.6 ft and is currently at rest. The damping force is 9 ˙x and an external force of 2 cos 4t applied. Set up the differential equation, including the initial conditions, but you do not need to solve.

The mean weight of newborn babies in a Long Island Community is 7.5 lbs. with a...

The mean weight of newborn babies in a Long Island Community is 7.5 lbs. with a standard deviation of 1.4 lbs. What is the probability that a random sample of 49 babies has a mean weight of at least 7.2 lbs?

The sample birth weight of 16 infants in a local community is 7.5 lbs with a...

The sample birth weight of 16 infants in a local community is 7.5 lbs with a standard deviation of 1.5 lbs. A census has revealed that national birth weight is 6,5 lbs. 1. Compute the test statistic to test if the average birth weight in the local community differs from that of the national average. Leave your answer correct up to 3 decimal places. 2. State the critical value(s) to test the above hypothesis at alpha=.01 a. ± 2.947 b....

A machine with a rotating shaft has a total weight of 200 lbs, and is supported...

A machine with a rotating shaft has a total weight of 200 lbs, and is supported by springs. The damping constant for the system is found to be 3 lb.sec/in. The resonant speed is determined exprimentally to be 1200 rpm, and the corresponding amplitude of the main mass of the machine is 0.50 inches. (a) Determine the amplitude for a speed of 2400 rpm. (b) Determine the fixed value which amplitude will eventually approach at high speed. (c) Determine the...

1. Assume that the average weight of an NFL player is 245.7 lbs with a standard...

1. Assume that the average weight of an NFL player is 245.7 lbs with a standard deviation of 34.5 lbs. The distribution of NFL weights is not normal. Suppose you took a random sample of 32 players. What is the probability that the sample average will be between 242 and 251 lbs? Round your answer to three decimal places, eg 0.192. 2. Given a sample with a mean of 57 and a standard deviation of 8, calculate the following probabilities...

Question