38 Lecture

The formula for work when the force applied is not constant is:

A) W = F(x)dx

B) W = F(x)dy

C) W = F(x)dt

D) W = F(x)ds

Answer: A) W = F(x)dx

The unit of work is:

A) Joule

B) Meter

C) Newton

D) Watt

Answer: A) Joule

How do you calculate the work done when the force applied is in the opposite direction of the displacement?

A) Positive

B) Negative

C) Zero

D) None of the above

Answer: B) Negative

The work done over a small interval of distance is calculated as:

A) dW = F(x)dy

B) dW = F(x)dt

C) dW = F(x)ds

D) dW = F(x)dx

Answer: D) dW = F(x)dx

How do you calculate the work done when the force applied is perpendicular to the displacement?

A) Positive

B) Negative

C) Zero

D) None of the above

Answer: C) Zero

What is the formula for work when lifting a weight to a certain height?

A) W = ?[a,b] F(x)dx

B) W = ?[a,b] F(h)dh

C) W = Fd

D) W = mg*h

Answer: B) W = ?[a,b] F(h)dh

What does the definite integral represent in the context of work?

A) Total force applied

B) Total distance covered

C) Total work done

D) Total displacement

Answer: C) Total work done

How do you find the total work done when the force applied is constant?

A) W = Fd

B) W = ?[a,b] F(h)dh

C) W = ?[a,b] F(x)dx

D) W = mg*h

Answer: A) W = F*d

How do you calculate the work done over a small interval of height?

A) dW = F(x)dx

B) dW = F(x)dy

C) dW = F(h)dh

D) dW = F(x)ds

Answer: C) dW = F(h)dh

What is the formula for work when the force applied is in the same direction as the displacement?

A) Positive

B) Negative

C) Zero

D) None of the above

Answer: A) Positive

What is the formula for work when the force applied is not constant?

Answer: The formula for work when the force applied is not constant is W = ?[a,b] F(x)dx, where F(x) is the force applied at a point x and dx is a small interval of distance.

How do you calculate the work done over a small interval of distance?

Answer: The work done over a small interval of distance is calculated as dW = F(x)dx, where F(x) is the force applied at a point x and dx is a small interval of distance.

What is the relationship between the area under the force-distance curve and the total work done?

Answer: The area under the force-distance curve represents the total work done.

What is the formula for work when lifting a weight to a certain height?

Answer: The formula for work when lifting a weight to a certain height is W = ?[a,b] F(h)dh, where F(h) is the force required to lift the weight to a height h and dh is a small interval of height.

How do you calculate the work done over a small interval of height?

Answer: The work done over a small interval of height is calculated as dW = F(h)dh, where F(h) is the force required to lift the weight to a height h and dh is a small interval of height.

What does the definite integral represent in the context of work?

Answer: The definite integral represents the total work done over a distance or height.

How do you find the total work done when the force applied is constant?

Answer: When the force applied is constant, the total work done is calculated as W = F*d, where F is the constant force and d is the distance over which the force is applied.

What is the unit of work?

Answer: The unit of work is joule (J).

How do you calculate the work done when the force applied is in the opposite direction of the displacement?

Answer: When the force applied is in the opposite direction of the displacement, the work done is negative.

How do you calculate the work done when the force applied is perpendicular to the displacement?

Answer: When the force applied is perpendicular to the displacement, the work done is zero.

In calculus, the concept of work involves the application of force over a certain distance. This concept is important in physics, engineering, and other fields where work is a fundamental aspect of many processes. In order to calculate the amount of work done, we can use the concept of definite integrals. The basic formula for work is W = F * d, where W is the amount of work done, F is the force applied, and d is the distance over which the force is applied. However, in many situations, the force applied may not be constant over the entire distance, which means we need to use calculus to find the total work done. The idea behind using calculus to find the total work done is to break the distance over which the force is applied into small intervals, and calculate the work done over each interval. We can then add up the work done over all the intervals to find the total work done. Mathematically, we can express this concept using definite integrals. Let's consider an example. Suppose we want to find the amount of work required to move an object from point A to point B, where the force applied is not constant. We can break the distance from A to B into small intervals, and calculate the work done over each interval. If we let F(x) be the force applied at a point x, and dx be a small interval of distance, then the work done over that interval is: dW = F(x) * dx To find the total work done, we need to integrate this expression over the entire distance from A to B. The definite integral that represents the total work done is: W = ?[A,B] F(x) dx This formula tells us that the work done is equal to the area under the force-distance curve between points A and B. The curve represents the variation of the force over the distance, and the area under the curve represents the total work done. Let's consider another example. Suppose we want to find the amount of work required to lift a 10-pound weight to a height of 5 feet. We can use the formula W = F * d, where F is the force required to lift the weight and d is the distance over which the weight is lifted. In this case, F varies with height, so we need to use calculus to find the total work done. Let F(h) be the force required to lift the weight to a height h, and dh be a small interval of height. Then the work done over that interval is: dW = F(h) * dh To find the total work done, we need to integrate this expression over the entire height of 5 feet. The definite integral that represents the total work done is: W = ?[0,5] F(h) dh This formula tells us that the work done is equal to the area under the force-height curve between heights 0 and 5 feet. In conclusion, the concept of work is important in many fields, and in situations where the force applied is not constant, we need to use calculus to find the total work done. Definite integrals allow us to calculate the work done by breaking the distance over which the force is applied into small intervals and summing up the work done over each interval. The area under the force-distance or force-height curve represents the total work done, and the definite integral allows us to calculate this area.