Find −→F2 at that instant.
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: A particle of mass m has the following position vector as a function of time t r(t) = At3ˆi + Bt2ˆj + Ctˆk where A, B, and C are constants. At t = τ , two external forces −→F1 =αˆi+βˆj+γ ˆk and −→F2 act on the particle where α, β, and γ are constants. Find −→F2 at that instant.

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- Shown to the right is a block of mass m resting on a frictionless ramp inclined at an angle to the horizontal. The block is held by a spring that is stretched a distance d after the block is attached to it. E k= e wwwwww ▷ A Write an equation for the force constant of the spring in terms of the variables from the problem statement (m, 0, and d). Use g for the gravitational constant.A particle, which remains at rest, is acted on by three forces, P, Q and R, and no others, as shown in the diagram attached. The force P acts horizontally to the left, the force Q acts vertically upwards and the force R acts downwards and to the right at an angle of 30◦ to the horizontal. The magnitude of P is 52 N. Let the magnitudes of Q and R in newtons be Q and R respectively. Take the Cartesian unit vectors i and j to be in the opposite direction to P and in the same direction as Q, respectively. a) Find expressions for the component forms of the three forces P, Q and R. b) Hence or otherwise find Q to two significant figures.A block with weight 50 N stops on an inclined plane which has angle 0 = 30° to the horizontal. Two observers try to analyse the forces on the block with their preferred reference. Observer A uses coordinate (xẠ, YA) as his reference while observer B uses coordinate (Xg, Yg) as her reference(See figure 1). YA Observer A Block Observer B XA W XB Figure 1. (a) Decompose the weight, W and the normal force, Ñ in the coordinate system of observer A. (b) Decompose the weight, W and the normal force, Ñ in the coordinate system of observer B. (c) Determine the magnitude of friction obtained by A and B respectively if the block tends to slide down. (d) Are the two answers in part (c) same or different? What does the result imply?
- A particle of mass m is located at the origin. It is at rest and in equilibrium. A time-dependent force of F → (t) is applied at time t = 0 , and its components are Fx(t) = pt and Fy(t) = n + qt where p, q, and n are constants. Find the position r → (t) and velocity v → (t) as functions of time t.A particle of mass 25 kg moves in a straight line such that the force (in Newtons) acting on it at time ₺ (in seconds) is given by 225 to +175 + + 200. If at time t = 0 its velocity, v (in ms-¹), is given by v(0) = 14, and its position (in m) is given by (0) = 10, what is the position of the particle at time t? l The position is m.A block, initially at rest, has a mass m and sits on a plane inclined at angle theta. It slides a distance d before hitting a spring and compresses the spring by a maximum distance of xf. If the coefficient of kinetic friction between the plane and block is uk, then what is the force constant of the spring?
- A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 5.80-kg puck has a velocity of 2.001 m/s at one instant. Eight seconds later, its velocity is (6.001 + 8.0ĵ) m/s. (a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force. Î + (b) Find its magnitude. NA lazy fish sees your fishing hook. The fish is initially located at position (3 m,-2 m) and drifts towards the fishing hook that is located at position (6 m, 0 m). The fish is a real lunker and has a mass of m = 9.1 kg. a) What is the displacement vector for the fish during this time interval? Express your answer using unit-vector notation (i.e. ->Ar = _î + __j) (6 m, 0 m) |(3 m, -2 m) Suppose the river exerted a constant force of F* = (28 N)î – (14 N)ĵ on the fish as it moved toward the hook. b) How much work was done on the fish by the river?Two objects (m1=11.0 kg and m2=3.00 kg) are separated by 40.0 cm. A third object (m3=1.00 kg) is placed at a location along the line connecting them such that the net force acting on it is zero. By considering the force vectors, this location must be between the two original objects. We will define x as the distance between m1 and m3 and y as the distance between m2 and m3. 1) Find the distance between 11.0-kg object and 1.00-kg object along the line AB where a small, 1.00-kg object could rest such that the net gravitational force on it due to the two objects shown is exactly zero. (Express your answer to two significant figures.)
- A massless spring with spring constant 26 N/m hangs vertically. A body of mass 1.0 kg is attached to its free end and then released. Assume that the spring was unstretched before the body was released. Find how far below the initial position the body descends. I don't understand why I'm getting this first part wrong specifically because the formula is just x= mg/k because F=kx.A particle of mass 1.05 kg is subject to a force that is always pointed towards the East but whose magnitude changes linearly with time t. The magnitude of the force is given as F = 4t, and has units of newtons. Let the x-axis point towards the East. Determine the change in x-coordinate in meters of the particle Δx between t = 0 and t = 2.4 if the initial velocity is 17.5 m/s, and pointed in the same direction as the force.Here we have a block of mass (m=2.50kg) resting on a place inclined at an angle of ø=30° to the horizontal. The coefficient of static friction between the block and the plane is Ustatic = 0.135 and the block is stationary but just on the point of sliding up the slope. The diagram shows the four forces acting on the block: an applied force F1 acting up the slope, the block's weight mg, the normal reaction force N and the force of static friction, Ff. In this case, the force of static friction acts down the slope, opposing the tendency of the block to move up the slope. Find the the maximum magnitude of the applied force F1 that can be exerted if the block is to remain stationary.