A 1.5−kg block rests on top of a 2−kg block supported by, but not attached to, a spring of constant 40 N/m. The upper block is suddenly removed. Determine the maximum speed reached by the 2−kg block. The maximum speed reached by the 2−kg block is m/s. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
A smooth pulley is used to drag a mass 25.5 kg up a slope. The coefficient of dynamic friction between the mass and the slope is 0.410. A second mass of 20.8 kg is attached to the end of the rope. A person pulls downwards with an additional force of 315 N on a second rope as shown in the diagram. Calculate the acceleration in ms−2 of the 25.5 kg mass. Give your answer with units to an appropriate number of significant figures. Assume the mass of the rope is negligible.
Two small objects each of mass m = 0.6 kg are connected by a lightweight rod of length d = 0.7 m (see the figure). At a particular instant they have velocities whose magnitudes are v1 = 37 m/s and v2 = 57 m/s and are subjected to external forces whose magnitudes are F1 = 73 N and F2 = 32 N. The distance h = 0.2 m, and the distance w = 0.8 m. The system is moving in outer space. (a) What is the total (linear) momentum P→total of this system? P→total = kg⋅m/s (b) What is the velocity v→cm of the center of mass? v→cm = m/s (c) What is the total angular momentum L→A of the system relative to point A? L→A = kg⋅m2 /s (d) What is the rotational angular momentum L→rot of the system? L→rot = kg⋅m2 /s (e) What is the translational angular momentum L→trans of the system relative to point A? L→trans = kg⋅m2 /s (f) After a short time interval Δt = 0.23 s, what is the total (linear) momentum P→ total of the system? P→total = kg⋅m/s
At a particular instant, a 1.0 kg particle's position is r→ = (4.0 i^−5.0 j^+2.0 k^)m, its velocity is v→ = (−1.0 i^+5.0 j^+1.0 k^)m/s, and the force on it is F→ = (13.0 i^+17.0 j^)N. (Express your answers in vector form.) (a) What is the angular momentum (in kg⋅m2 /s) of the particle about the origin? ı→ = kg⋅m2 /s (b) What is the torque (in N⋅m) on the particle about the origin? τ→ = N⋅m (c) What is the time rate of change of the particle's angular momentum about the origin at this instant (in kg⋅m2 /s2)? dl→dt = kg⋅m2 /s2
A uniform bar of mass M = 28.2 kg has a mass m = 10.4 kg attached three quarters of the way from its left end. The bar is supported in equilibrium by two vertical ropes at the left and right ends under tension T1 and T2 respectively. The bar has a length L = 4.11 m. This is shown in the diagram. (The input below will accept answers with no more than 1% variation from the correct value.) What is T1? N What is T2? N
The figure shows three electric charges. The charge Q1 is 6.24×10−6 C and is at the point x = 0 and y = L = 1.89×10−2 m, Q2 is 3.43×10−6 C and is at the point x = 0, y = −L = −1.89×10−2 m, and Q3 is −2.70×10−6 C and is at y = 0 and x = 2 L, twice the distance from the origin as Q1 and Q2. What is the y-component of the total force on the charge Q3? Give your answer in Newtons to 2 decimal places. Do not include units in your answer. Be sure to use the sign of your answer to indicate direction. Your answer should be positive if the force is upwards, and negative if the force is downwards.
Problem 2: Coulomb's law and multiple point charges Three point-charges are arranged as in the picture. Charge q is known to be positive, while charges Q1 and Q2 are unknown. We know however some information about them: the net force they exert on q points downwards, along the −y-axis as shown. A. Is Q1 positive, negative or could it have either sign? Explain. (Hint: How does Q1 contribute to F→net ?) B. Is Q2 positive, negative or could it have either sign? (Hint: How do Q2 and Q1 contribute to F→net ?)
An electron follows a helical path in a uniform magnetic field of magnitude 5 T. The pitch of the path (d in the figure below) is 6 μm, and the magnitude of the magnetic force on the electron is 3×10−15 N. What is the electron's speed (in km/s)?
A thin rod of length L = 2 m, mass m = 3 kg, and moment of inertia I = 4.0 kg⋅m2 is hinged at the top. It is held in place at an angle θ = 40∘ to the horizontal by a horizontal wire, as shown at right. The wire is attached to the rod a distance z = 1.6 m from the hinge. The hinge exerts a force on the top of the rod as well as a constant magnitude frictional torque τ = 5 N⋅m that (along with the wire) tries to keep the rod from rotating. The wire is cut at time t = 0.2) What is the tension in the wire for t < 0? (Yes, you include the frictional torque in your analysis). 3) What is the horizontal component of the force exerted by the hinge on the rod just after the wire is cut? 4) What is the angular speed of the rod when it is vertical for the first time?
(a) Three point charges are located on the circumference of a circle of radius r, at the angles shown in the figure. What is the electric field at the center of the circle due to these point charges? (Express your answer in vector form. Use the following as necessary: ke, q, and r.) E→ = (b) What If? What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with a minimum separation of 6.10∘ between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a). Eminimum Epart (a) =