Assn. 4

A force F = bx3 acts in the x-direction, where the value of b is 3.7 N/m3. How much work is done by this force in moving an object from x = 0 m to x = 2.6 m?

42 J (∫(from 0 to 2.6) 3.7x^3)

A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?

Both objects travel the same distance.

A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on the object during a displacement from x = -2.00 m to x = 2.00 m. (Assume an accuracy of 3 significant figures for the numbers on the graph.)

-1 J

In the figure, a 700-kg crate is on a rough surface inclined at 30°. A constant external force P = 5600 N is applied horizontally to the crate. As the force pushes the crate a distance of 3.00 m up the incline, the speed changes from 1.40 m/s to 2.50 m/s. How much work does gravity do on the crate during this process?

-10,300 J

A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at a constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do?

1.26 kJ

Determine the scalar product of A=6 i + 4 j -2 k and B = 5 i - 6 j -3 k.

12 (6*5 + 4*(-6) + (-2)*(-3))

A spring stretches by 21 cm when a 135 N object is attached. What is the weight of a fish that would stretch the spring by 31 cm?

199 N

A 7.0-kg rock is subject to a variable force given by the equation F(x) = 6.0 N - (2.0 N/m)x + (6.0 N/m2)x2 If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.

20 m/s

A force on a particle depends on position such that F(x) = (3.00 N/m2)x2 + (6.00 N/m)x for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from x = 0.00 m to x = 2.00 m?

20.0 J

A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on an object that moves from x = 1.0 m to x = 6.0 m. (Assume an accuracy of 2 significant figures for the numbers on the graph.)

26 J

A crane lifts a 425 kg steel beam vertically a distance of 117 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s2? Neglect frictional forces.

5.8 × 10^5 J 425 x (9.8+1.8) = 4930 4930 x 117 = 576810

The work performed as a function of time for a process is given by W =at3 where a= 2.4 J/S3.What is the instantaneous power output at t = 3.7 s?

99W 3bt^2 = 3*2.4*(3.7)^2 = 98.5

Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do.

Neither of them does any work.

If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.

True

Which of the graphs in the figure illustrates Hooke's Law?

XX c (straight line gown down & to the right, in the 4th quadrant) XX

Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring. The slope of the curve would be

XX the reciprocal of the spring constant. XX