A certain atom has 82 protons. Assume that the nucleus is a sphere with radius 6.84 fm and with the charge of the protons uniformly spread through the sphere. At the nucleus surface what are (a) the magnitude and (b) direction (radially inward or outward) of the electric field produced by the protons? (a) Number Units (b)
The figure shows a 0.3 kg baseball just before and just after it collides with a bat. Just before, the ball has velocity v→1 of magnitude 10.8 m/s and angle θ1 = 33.9∘. Just after, it is traveling directly upward with velocity v→2 of magnitude 8.90 m/s. The duration of the collision is 2.60 ms. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the impulse on the ball from the bat? What are the (c) magnitude and (d) direction of the average force on the ball from the bat? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The 150- kg lunar lander is descending onto the moon's surface with a velocity of 4.1 m/s when its retro-engine is fired. If the engine produces a thrust T for 5.4 s which varies with the time as shown and then cuts off, calculate the velocity of the lander when t = 6.1 s assuming that it has not yet landed. Gravitational acceleration at the moon's surface is 1.62 m/s2. The velocity is positive if moving downward, negative if up. Answe: v = m/s
Starting with an initial speed of 5.86 m/s at a height of 0.116 m, a 1.69-kg ball swings downward and strikes a 4.36-kg ball that is at rest, as the drawing shows. (a) Using the principle of conservation of mechanical energy, find the speed of the 1.69-kg ball just before impact. (b) Assuming that the collision is elastic, find the velocity (magnitude and direction) of the 1.69-kg ball just after the collision. (c) Assuming that the collision is elastic, find the velocity (magnitude and direction) of the 4.36-kg ball just after the collision. (d) How high does the 1.69−kg ball swing after the collision, ignoring air resistance? (e) How high does the 4.36-kg ball swing after the collision, ignoring air resistance? (a) Number Units (b) Number Units (c) Number Units
Two point charges q1 = +2.45 nC and q2 = −2q1 are located along the x-axis as shown in the diagram below. The distance between the two charges is d = 1.65 m. (a) Which of the following graphs correctly represents the total electric potential versus x for the region −2.50 m < x < 2.50 m? (b) At what location A between the two charges on the x-axis will the electric potential be zero? m
The figure shows a 0.300 kg baseball just before and after it collides with a bat. Just before, the ball has a velocity v1 of magnitude 12.8 m/s and angle θ1 = 35°. Just after, it is travelling directly upward with velocity v2 of magnitude 10.0 m/s. The duration of the collision is 1.60 ms. (a) What is the magnitude of the impulse on the ball from the bat? kg⋅m/s (b) What is the direction (relative to the positive direction of the x axis) of the impulse on the ball from the bat? ° (counterclockwise from the +x axis) (c) What is the magnitude of the average force on the ball from the bat? N (d) What is the direction of this average force? ° (counterclockwise from the +x axis)
Review Conceptual Example 11 before attempting to work this problem. Four charges with equal magnitudes of 7.28×10−12 C are placed at the corners of a rectangle. The lengths of the sides of the rectangles are 2.52 cm and 4.16 cm. Find the magnitude of the electric field at the center of the rectangle in Figures a and b. (a) (b) (a) Number Units (b) Number Units
Two separate sets of parallel plates are in a vacuum, as shown in the diagram below. A negatively-charged ion that has 2 extra electrons and a mass of (5.550×10^−26) kg, essentially at rest, drifts into the hole in plate X and is accelerated to the right. The vertical motion of the ion continues to be negligible. The electron passes through holes W and Y, then continues moving forward, eventually colliding with plate Z. where ΔV1 = (8.97×10^2) V and ΔV2 = (3.669×10^2) V Note: Gravitational effects are negligible. The speed that the ion hits plate Z at is m/s. Round and record your answer to
A bead on a spinning hoop: angle and maximum period Note: For this problem, please use g = 9.81 m/s2. Otherwise your answer may lie outside the numerical tolerance. A single bead can slide with negligible friction on a wire that is bent into a circle of radius 15.3 cm, as seen in the figure below. The circle is always in a vertical plane and rotates steadily about its vertical diameter. The position of the bead is described by the angle θ that the radial line from the centre of the loop to the bead makes with the vertical. 8 a If the loop is rotating with a period of 0.409 s, at what angle up from the lowest point can the bead stay motionless relative to the turning circle? Give your answer in degrees.
Problem X.4.3) Two bricks are pushed across a table with constant acceleration a as shown below. Brick A has twice the mass of brick B. The hand pushes horizontally, and there is no friction between the bricks and the table. (a) Compare the net force on A to that on B. How do you arrive at your conclusion? (b) Draw separate free-body diagrams for A and B. Make sure the label for each force indicates the types of force, the object on which the force is exerted, and the object exerting the force. (c) Is the magnitude of the force exerted by A on B greater than, less than, or equal to the force exerted by B on A? (d) Identify any third law pairs appearing in your two free-body diagrams. Is your answer to (c) consistent with these? (e) If the mass of brick B is m, determine the magnitude of all the forces in your free-body diagrams.