
(a)
The angle between the vectors
(a)

Answer to Problem 12P
The angle between the vectors
Explanation of Solution
Given that
Write the expression for dot product of
Here,
Rearrange equation (I), to find
Conclusion:
Substitute
Therefore, The angle between the vectors
(b)
The angle between the vectors
(b)

Answer to Problem 12P
The angle between the vectors
Explanation of Solution
Given that
Conclusion:
Substitute
Therefore, The angle between the vectors
(c)
The angle between the vectors
(c)

Answer to Problem 12P
The angle between the vectors
Explanation of Solution
Given that
Conclusion:
Substitute
Therefore, The angle between the vectors
Want to see more full solutions like this?
Chapter 6 Solutions
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
- Two gliders are set in motion on an air track. A light spring of force constant k is attached to the back end of the second glider. As shown in the figure below, the first glider, of mass m₁, moves to the right with a speed V₁, and the second glider, of mass m₂, moves more slowly to the right with a speed, V2. VI m2 i When m₁ collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of V1, V2, m₁, m2, and k, find the following. (Use any variable or symbol stated above as necessary.) (a) speed v at maximum compression V = (b) the maximum compression Xmax Xmax = (c) the speed of each glider after m₁ V1f = has lost contact with the spring (Use any variable or symbol stated above as necessary.) V2farrow_forwardAs shown below, a bullet of mass m and speed v is fired at an initially stationary pendulum bob. The bullet goes through the bob, and exits with a speed of pendulum bob will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the bob.) 2 The pendulum bob is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the V = L m M v/2 iarrow_forwardAs shown in the figure, a billiard ball with mass m₂ is initially at rest on a horizontal, frictionless table. A second billiard ball with mass m₁ moving with a speed 2.00 m/s, collides with m2. Assume m₁ moves initially along the +x-axis. After the collision, m₁ moves with speed 1.00 m/s at an angle of 0 = 48.0° to the positive x-axis. (Assume m₁ = 0.200 kg and m₂ = 0.300 kg.) m₁ Before the collision Vli After the collision Mi sin 9 Jif "If cos Vof COS U2f sin o Mo b (a) Determine the speed (in m/s) of the 0.300 kg ball after the collision. m/s (b) Find the fraction of kinetic energy transferred away or transformed to other forms of energy in the collision. |AKI K;arrow_forward
- A block with mass m₁ = 0.600 kg is released from rest on a frictionless track at a distance h₁ = 2.55 m above the top of a table. It then collides elastically with an object having mass m₂ = 1.20 kg that is initially at rest on the table, as shown in the figure below. h₁ իջ m m2 (a) Determine the velocities of the two objects just after the collision. (Assume the positive direction is to the right. Indicate the direction with the signs of your answers.) V1= m/s m/s (b) How high up the track does the 0.600-kg object travel back after the collision? m (c) How far away from the bottom of the table does the 1.20-kg object land, given that the height of the table is h₂ = 1.75 m? m (d) How far away from the bottom of the table does the 0.600-kg object eventually land? marrow_forwardAn estimated force-time curve for a baseball struck by a bat is shown in the figure below. Let F F(N) Fmax TÀ 0 t (ms) 0 la (a) the magnitude of the impulse delivered to the ball N.S (b) the average force exerted on the ball KN = 17,000 N, t = max a 1.5 ms, and t₁ = 2 ms. From this curve, determine the following.arrow_forwardThere are many well-documented cases of people surviving falls from heights greater than 20.0 m. In one such case, a 55.0 kg woman survived a fall from a 10th floor balcony, 29.0 m above the ground, onto the garden below, where the soil had been turned in preparation for planting. Because of the "give" in the soil, which the woman compressed a distance of 15.0 cm upon impact, she survived the fall and was only briefly hospitalized. (a) Ignoring air resistance, what was her impact speed with the ground (in m/s)? m/s (b) What was the magnitude of her deceleration during the impact in terms of g? g (c) Assuming a constant acceleration, what was the time interval (in s) during which the soil brought her to a stop? S (d) What was the magnitude of the impulse (in N⚫ s) felt by the woman during impact? N⚫s (e) What was the magnitude of the average force (in N) felt by the woman during impact? Narrow_forward
- Example Two charges, one with +10 μC of charge, and another with - 7.0 μC of charge are placed in line with each other and held at a fixed distance of 0.45 m. Where can you put a 3rd charge of +5 μC, so that the net force on the 3rd charge is zero?arrow_forward* Coulomb's Law Example Three charges are positioned as seen below. Charge 1 is +2.0 μC and charge 2 is +8.0μC, and charge 3 is - 6.0MC. What is the magnitude and the direction of the force on charge 2 due to charges 1 and 3? 93 kq92 F == 2 r13 = 0.090m 91 r12 = 0.12m 92 Coulomb's Constant: k = 8.99x10+9 Nm²/C² ✓arrow_forwardMake sure to draw a Free Body Diagram as wellarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning





